Capacity, spout and handle
The first question is capacity. Below a litre you are in carafe territory: fine for water on a laid table, too small for a group. Between one and one and a half litres is the usual size for home use and for table service. From two litres upwards you enter the hospitality format, and then it is worth checking whether the filled weight is still comfortable to lift, because a good two kilos on a single handle is more than it looks.
Then look at the spout and the handle. A proper pouring lip lets the last centilitres run out without dripping; a jug with nothing more than a pulled rim rarely manages that. A closed handle with room for four fingers pours more steadily than an open grip. And mind the wall thickness: thick-walled jugs keep cold drinks at temperature noticeably longer, even once the ice has melted.